Non-Integrability of Two-Dimensional QCD

TL;DR

This paper numerically shows that massless two-dimensional QCD is not integrable by solving the 't Hooft equation and analyzing decay amplitudes, which are non-zero except when involving pions.

Contribution

It introduces an adaptive spline method to solve the 't Hooft equation and provides numerical evidence of non-integrability in 2D QCD.

Findings

Decay amplitudes are generally non-zero, indicating non-integrability.

Decay amplitudes vanish only when decay involves a pion.

Numerical solutions confirm non-integrability of massless 2D QCD.

Abstract

In this paper we numerically demonstrate that massless two-dimensional QCD is not integrable. To this aim, we explicitly solve the 't Hooft integral equation for bound states by an adaptive spline procedure, and compute the decay amplitudes. These amplitudes significantly differ from zero except in all cases in which the decay also produces a pion.